General \(2\times 2\)  matrix games are often defined by the ordering of the four payoff matrix entries from table REF  (see e.g. [1]}, [2]}). Even though there are 24 possible orderings, pairs of orderings having \(b\)  and \(c\)  swapped as well as \(a\)  and \(d\)  correspond to the same game with the definition of strategies \(A\)  and \(B\)  swapped. Therefore, there are a total of 12 independent \(2\times 2\)  games, each with a pair of complementary orderings. These pairs are shown together in table  and delimited by horizontal lines. Strategy \(A\)  in each ordering is considered the mutant and \(B\)  is considered the resident.
